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Physical review. B, Condensed matter

Spin gap and paired wave function for the frustrated antiferromagnetic spin- 12 zigzag ladder

Zou Ha

Published Jan 15, 1999• 6 citations
Publisher

Abstract

I propose a BCS-like paired wave function for the spin-gap phase of the zigzag spin-1/2 ladders. A single parameter family of the proposed wave function can be made to continuously interpolate from the gapless spin-liquid state to the fully dimerized Majumdar-Ghosh state or from the weak- to the strong-coupling spin-paired states. The family of wave function clearly illuminates the nature of spin pairing in the spin-gap phase.

DOI
10.1103/physrevb.59.1559

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I propose a BCS-like paired wave function for the spin-gap phase of the zigzag spin-1/2 ladders. A single parameter family of the proposed wave function can be made to continuously interpolate from the gapless spin-liquid state to the fully dimerized Majumdar-Ghosh state or from the weak- to the strong-coupling spin-paired states. The family of wave function clearly illuminates the nature of spin pairing in the spin-gap phase.
I propose a new paired-wavefunction with a parameter that continuously interpolates from the 1D Jastrow-product to the Majumdar-Ghosh dimer-wavefunction appropriate for the frustrated Heisenberg S=1/2S = 1/2S=1/2 antiferromagnet. This spin paired-state constructed in SzS_zSz​ basis is an alternative to the well-known resonating-valence-bond basis state for describing the S=0S = 0S=0 ground-state with no apparent long-range spin order. Some numerical evidences are presented.
We investigate an asymmetric zigzag spin ladder with different exchange integrals on both legs using bosonization and renormalization group approaches. When the leg exchange integrals and frustration both are sufficiently small, renormalization group analysis shows that the Heisenberg critical point flows to an intermediate-coupling fixed point with gapless excitations and a vanishing spin velocity. When they are large, a spin gap opens and a dimer liquid is realized. Here, we find a continuous manifold of Hamiltonians with dimer product ground states, interpolating between the Majumdar-Ghosh and sawtooth spin-chain model.
We perform a systematic investigation on an asymmetric zigzag spin ladder with interleg exchange J1{J}_{1}J1​ and different exchange integrals ${J}_{2}\ifmmode\pm\else\textpm\fi{}\ensuremath{\delta}$ on both legs. In the weak frustration limit, the spin model can be mapped to a revised double frequency sine-Gordon model by using bosonization. Renormalization-group analysis shows that the Heisenberg critical point flows to an intermediate-coupling fixed point with gapless excitations and a vanishing spin velocity. When the frustration is large, a spin gap opens and a dimer ground state is realized. Fixing J2=J1/2,{J}_{2}{=J}_{1}/2,J2​=J1​/2, we find, as a function of $\ensuremath{\delta},$ a continuous manifold of Hamiltonians with dimer product ground states, interpolating between the Majumdar-Ghosh and sawtooth spin-chain model. While the ground state is independent of the alternating next-nearest-neighbor exchange $\ensuremath{\delta},$ the gap size of excitations is found to decrease with increasing $\ensuremath{\delta}.$ We also extend our study to a two-dimensional double layer model with an exactly known ground state.
The phase diagram of a frustrated spin-S zig-zag ladder is studied through different numerical and analytical methods. We show that for arbitrary S, there is a family of Hamiltonians for which a fully-dimerized state is an exact ground state, being the Majumdar-Ghosh point for a particular member of the family. We show that the system presents a transition between a dimerized phase to a Néel-like phase for S = 1/2, and spiral phases can appear for large S. The phase diagram is characterized by means of a generalization of the usual mean field approximation. The novelty in the present implementation is to consider the strongest coupled sites as the unit cell. The gap and the excitation spectrum is analyzed through the random phase approximation. Also, a perturbative treatment to obtain the critical points is discussed. Comparisons of the results with numerical methods like the Density Matrix Renormalization Group are also presented.
We show strong numerical evidence in favor of an unexpected virtually gapless spectrum, with edge states localized at the boundaries, in frustrated spin-1∕21∕21∕2 antiferromagnetic ladders with an odd number of legs. These features can be accurately reproduced by using a projected BCS wave function with a nontrivial pairing that mixes even and odd reflection symmetries. This approach gives the correct classification of the excitations and provides a simple and very appealing picture of an unconventional spin-liquid phase stabilized by frustration.
We study a family of frustrated antiferromagnetic $\text{spin}\ensuremath{-}S$ systems with a fully dimerized ground state. Starting from the simplest case of the frustrated zigzag spin ladder, we generalize the family to more complex geometries like tetrahedral ladders and spin tubes. After presenting some numerical results about the phase diagram of these systems, we show that the ground state is robust against the inclusion of weak disorder in the couplings as well as several kinds of perturbations, allowing to study some other interesting models as a perturbative expansion of the exact one. A discussion on how to determine the dimerization region in terms of quantum information estimators is also presented. Finally, we explore the relation of these results with the case of a four-leg spin tube, which recently was proposed as a model for the description of the compound Cu2Cl4D8C4SO2{\mathrm{Cu}}_{2}{\mathrm{Cl}}_{4}{\mathrm{D}}_{8}{\mathrm{C}}_{4}{\mathrm{SO}}_{2}Cu2​Cl4​D8​C4​SO2​, delimiting the region of the parameter space where this model presents dimerization in its ground state.